hard to say exactly what temp it will get to, all depends on aerodynamics, mass and shape of the rim, speeds at which wheel is moving, frequency of heat output, amount of heat generated, etc etc. if i drive w/o ever hitting the brakes, rim will be at ambient. but if i go 40-100mph and 100-40mph every 60 sec then the rim will get very hot.

i guess all i can say is, rim will be lower in temp then rotor hub. if you are looking for equations then it will be a heatsink problem with complex functions because you'll need to model the heatsink (rim) properly, which has many variables.

you watch tonight when 3000 pound plus NASCAR racers run the worlds fastest 1/2 mile bull ring. Right front brake rotors go excess 1400 to 1500 degree F for 500 miles. The wheel gets super hot as does the tire beads. Multiple air cooling fans and cooling ducts are used. You will see the rotors glow red during the race.
Street car typical temps are as the brake pad manufacturers plan up to 300 degree C per attached graph